In Section  we define a notion of pentaction of any object \(A\in \mathbf {rGr}^{\bullet }\) . The notion of perfect objects of \(\mathbf {rGr}^{\bullet }\)  is introduced and an example is given. This notion is an analogue of perfect algebras in the categories of associative and Leibniz algebras, respectively. This property is a sufficient condition for the existence of an actor for the objects in these categories [1]}, [2]}. Then we introduce notions of stabilizer and weak stabilizer of an object \(A\in \mathbf {rGr}^{\bullet }\)  denoted by \(\mathsf {Stab}(A)\)  and \(\mathsf {wStab}(A)\) , respectively. The prototype of stabilizer of \(A\)  is annihilator in the case of algebras; recall that \(\mathsf {Ann}(A)=0\)  is a sufficient condition for the existence of actor in the categories of associative and Leibniz algebras (see e.g. [1]}, [2]}). We give an example of an object of \(\mathbf {rGr}^{\bullet }\)  which is perfect with zero weak stabilizer. It is proved that if \(A\)  is perfect with \(\mathsf {wStab}(A)=0\) , then \(\mathsf {Pentact}(A)\)  is an object of \(\mathbf {rGr}^{\bullet }\)  (Theorem REF ).
